Because rocks have a certain rigidity, the displacement and velocity associated with pressure waves are not, for a given density, functions of the incompressibility alone, but also of the rigidity which links particles to each other.

In the shear waves, displacement occurs without volume change and the velocity is, for a given density, a function of rigidity alone.

For isotropic media:

V_p = <fr>(k + 4/3µ)^½</>^rgrv</fr> and V_s = (µ/^rgrv)^½

where V_p, V_s = velocities of pressure and shear waves; k = incompressibility modulus; µ = rigidity modulus; and ^rgrv = density.

The knowledge of V_p alone is not enough to separate the effects of changes of incompressibility and rigidity. Though seismic velocities are proportional to the reciprocal of the square root of the density, statistical evidence shows that pressure and shear-wave velocities increase with density.

This must be attributed mainly to the effect of cementation. Cementation fills pores with solid material, thus increasing incompressibility, and cements particles together, increasing rigidity. However, compaction, the process of volume reduction, has much less effect on the rigidity increase than on the incompressibility increase. Where cementation is not important, low shear-wave velocities can be expected. Lower shear-wave velocities can also be expected where fracturing decreases rigidity, or where the shaliness of a horizon increases. Compressibility changes can be detected in shaly intervals.

The velocity of pressure waves may remain fairly constant when ridigity increases and incompressibility decreases, as when voids occur where the matrix is better cemented than in contiguous formations. The knowledge of V_s might attract attention to such situations.

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